Inventory management problem: 1.Freeport Corporation finds that demand for surfb
ID: 393974 • Letter: I
Question
Inventory management problem:
1.Freeport Corporation finds that demand for surfboards has average demand of 10 units per day, with a standard deviation of 3 units. Lead time from the supplier averages 12 days, with a standard deviation of 2 days. The item costs $50 and the inventory carrying cost is 30%.
a. Suppose management decides to offer a 95% service level. That is, it is willing to experience a stockout probability of 5% during the order cycle. How much safety stock should be carried?
b. How much is the annual inventory carrying cost of the safety stock because of this decision?
c. You decide that you want this company to give better service to its customers. You decide that a 99% service level is appropriate. How much safety stock must be carried to offer this service level?
d. What is the additional inventory carrying cost that will be incurred on this item because of your decision to increase the service level?
Please show the math in details for each of the question
Explanation / Answer
Answer to question # a :
Service level = 95% ( i.e. 0.95 )
Corresponding z value = NORMSINV ( 0.95 ) = 1.6448
Standard deviation of demand during Lead time can be formulated as :
= Square root ( Standard deviation of daily demand^2 x Lead time + Daily demand^2 x Standard deviation of Lead time^2)
Basis above equation , standard deviation of demand during lead time
= Square root ( 3^2 x 12 + 10^2 x 2^2)
= Square root ( 108 + 400)
= Square root ( 508 )
= 22.54 ( rounded to 2 decimal places )
The quantum of safety stock which should be carried
= Z value x Standard deviation of demand during lead time
= 1.6448 x 22.54
= 37.07 ( rounded to nearest whole number 37)
Quantum of safety stock which should be carried = 37 surfboards
Answer to question # b :
Following to be noted :
Unit inventory carrying cost = 30% of item cost of $50 = $15
Therefore , annual inventory carrying cost of the safety stock
= Unit inventory carrying cost x Safety stock
= $15 x 37
= $555
Annual inventory carrying cost of the safety stock = $555
Answer to question # c :
The same calculation will be repeated for 99% service level ( as has been done for 95% service level)
Service level = 99 % ( 0r, 0.99 )
Corresponding Z value = 2.3263
Standard deviation of demand during lead time ( already calculated ) = 22.54
Therefore,
Safety stock = Z value x standard deviation of demand during lead time = 2.3263 x 22.54 = 52.54 ( rounded to nearest whole number 53 )
Safety stock that should be carried to offer this service level = 53
Answer to question d :
Additional safety stock due to increase in service level from 95% to 99%
= 53 - 37
= 16 surfboards
Therefore ,
Additional inventory cost that will be incurred because of increase in service level
= Unit inventory carrying cost x Additional safety stock
= $15 x 16
= $240
Additional inventory carrying cost = $240
Quantum of safety stock which should be carried = 37 surfboards
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